Nonlinear multi-parameter eigenvalue problems for systems of nonlinear ordinary differential equations arising in electromagnetics

Abstract

We investigate a generalization of one-parameter eigenvalue problems arising in the theory of nonlinear waveguides to a more general nonlinear multiparameter eigenvalue problem for a nonlinear operator. Using an integral equation approach, we derive functional dispersion equations whose roots yield the desired eigenvalues. The existence and distribution of roots are veried.